A Brooklyn mom of three was fatally gunned down this morning by a passerby as she stood right behind Brookdale Hospital — where her 8-year-old daughter was undergoing treatment for an asthma attack.

The apparently motiveless killing stunned the family of 32-year-old victim Shalema Gaskin — and left them demanding answers about why someone targeted her.

“This is a hospital!” said Tanya Gaskin, 50, the victim’s mom. “We come here for help — not to have our people killed right outside.”

Shalema Gaskin had brought her own 8-year-old daughter Saniyah Gaskin-Miley to Brookdale Hospital — which is just blocks from their home — yesterday morning when the child began suffering an asthma attack. The child’s dad accompanied them there.

While the child was still in the hospital early this morning, at around 3:10 a.m., Shalema left the hospital without telling other family members, including the child’s father, according to her relatives.

“My daughter came out outside, probably to smoke a cigarette,” said Shalema’s mom Tanya. “She didn’t tell anyone she was leaving, because she was planning on going back inside.”

While Gaskin stood outside the hospital on Hegeman Avenue and East 98th Street, a passerby shot her once in the neck and then calmly walked away, said cops, citing a witness.

She was rushed into the hospital, but later died there. In addition to Saniyah, Gaskin left behind two other daughters — an 18-year-old and a five-year-old.

Her shocked family had no idea why someone would shoot Gaskin, particularly because the shooter took nothing from her, including her iPhone.

“I want answers,” said Tanya Gaskin. “It’s not fair to have her life taken, and for no one to have answers.”

“All I want is my mom back,” the grieving girl said. “She was a great mother. If something was wrong, she always knew. She was always there when we needed her.”

“Whoever did this didn’t take anything,” Tamara said. “I have her iPhone right here. Why would someone do this?”

Shalema’s family said she was currently unemployed, but had previously worked for three year’s with the city’s immigration services office, and was looking to follow her mother into a careers as a security guard.

At the blood-spattered shooting scene, Shalema’s family set up a shrine of balloons, candles and three teddy bears — one for each of her daughters. She had recent joined New Jerusalem Baptist Church in Queens, and was attending every Sunday.

Detectives were searching yards of surrounding buildings today.

“We don’t know why she came down, but she came down and that’s when she was shot,” said Gaskin’s aunt, Sabrina Miller.

“My niece was a beautiful person. She didn’t have to go like this.”

“I want answers to who did this,” Miller said. “I’m not going to rest until I get answers.”